# Knights & Knaves question 28 -seemingly another possibility?

I am not familiar with those puzzles and I would like to find out do I miss some rules which are necessary for solving those puzzles?

Here is an example - 28 (What is the name of this book? R.M.Smullyan)

In this problem, there are only two people, A and B, each of whom is either a knight or a knave. A makes the following statement: "At least one of us is a knave." What are A and B?<

Let's suppose A's statement is true - then, of course, A is knight, B is knave.(This is the right answer in the book)

But let's suppose A's statement is false -

then 1) A is knave, as he is making false statement, as implying that one (B in that case) is knave but not saying anything about himself - so the answer would be A - knave, B- knight;

or 2) A's statement is still false, when saying that "at least one of us is a knave" when the truth is, BOTH of them are knaves?

So my question is, can knaves make part-truth/part-lies statements? Another confusing detail is this 'either' usage in the question - when it is said "'either' of whom", does that mean a total 4 possibilities or 2 :

1. A & B both knaves
2. A & B both knights (not in this puzzle)
3. A -knave, B - knight
4. A - knight, B -knave

Thank you.

• "at least one knave" means "one knave or both knaves". It is true unless neither is a knave – Henry Jan 3 '17 at 20:26
• Generally in these questions you are to assume that the knights speak only truths and the knaves speak only lies. Also, here, as elsewhere, "at least one" certainly includes "more than one". – lulu Jan 3 '17 at 20:26
• If you assume A is a knave, then "At least one of us is a knave is a true statement." Which a knave would never say, invalidating the assumption. – Doug M Jan 3 '17 at 20:27
• If I give you two dollars, and then I say later "I gave Aili at least one dollar", you may not complain that I have told a lie, or even a partial lie. I told the truth. – MJD Jan 3 '17 at 20:30